A ball of relative density 0.8 falls into water from a height of 2m. The depth to which the ball will sink is

Speed of the ball

 

= 6.32 m/s

Buoyancy force by water try to stop the ball. 

Buoyancy force = weight of displaced water

 = (d V)g

where d = density of water

V = volume of the ball  

g = 10 m/s2

deceleration of the body by buoyancy force, a = (dVg)/ m

where m= d'V

d' = density of block

a = dVg/(d' V)

= dg/d'

=(d/d')*g

=g/(0.8)

= 10/0.8  (Given, d'/d = 0.8)

= 12.5 m/s

Net deceleration of ball,a' = a-g = 2.5 m/s2

Final speed of ball v' = 0

Use v' 2 = v2 + 2a's 

s= depth of ball in the water

=> 40 = 0 + 2*2.5*s

=> s = 8m 

  • 40
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